This part is a straightforward adaption
of [1]}. Throughout the whole section \(f\)  is a meromorphic function satisfying all the hypotheses of Theorem REF .
We first give a fairly complete description of the behavior of the function \(f\)  near its poles and then we give the required upper estimate
of the Hausdorff dimension of \(\mathcal {I}_R(f)\)  for large \(R\) .
